Question

If p(x)=x^4-3x+2, then find the coefficient of the x^3 term in the polynomial (p(x))^3.

Answer 1

so ( p(x) )^3
= (x^4-3x+2)(x^4-3x+2)(x^4-3x+2)

now consider which combination can produce a term ending in x^3 ??

Answer 2

I don't understand what to do. Please clarify. Thank you.

Answer 3

If you were to fully expand this, your unsimplified line would consist of 27 terms
- that is, any combination of terms in the first bracket times any term in the second bracket times any term in the third bracket

the only way to get x^3 is to have
-3 from the first times -3x from the second times -3x from the third, or
-27x^3